In pricing a deal for an insurance contract or establishing a benchmark for a given industry segment, one of the main challenges is the quantification of the risk of losses in a high excess (“xs”) zone that might be well above the largest (trended) historical loss at hand. Almost always, high excess regions are the domain of reinsurance companies and a quantification as accurate as possible is simply crucial. A common technique called extrapolation consists in fitting the trended historical data and using the fit in the region beyond the historical losses. It is not known, however, whether this curve that fits well some data up to a few millions will correctly quantify the risk in regions that lie an order of magnitude above the last known loss, say at a hundred millions or even at one billion. Very much in the spirit of the credibility theory, one definitely has to rely on a greater set of data representative of the situation being considered for determining a relevant probability distribution for a high excess region. However, applying directly such a methodology to pricing a deal is lengthy and cumbersome since it involves each time collecting data from comparable industries, fitting the data, and mixing the fit with the one from the account loss history. Furthermore, an extrapolation of the industry data is also needed, which calls for collecting an even wider set of data. For a benchmark-type study the same issues need to be faced, starting one level higher. In the latter case the amount of work involved for a proper extrapolation may be a lot smaller in comparison with the size of the whole project itself, but the whole process would have to be repeated for each benchmark test, and the knowledge gained from this tailor-made extrapolation would not necessarily be considered as an independent result.